Arlie O. Petters

Birthplace: Dangriga, Belize

citizen. U.S. A.

B.A./M.A. (Mathematics and Physics) Hunter College 1986

Ph.D. (Mathematics) Massachusettes Institute of Technology 1991.

Area of Research Interests: Mathematical Physics

Read articles on Petters:

Full Professor of Physics and of Mathematics Departments of Duke University and a Bass Fellow.

**Petters's book on Gravitational Lensing is considered a
tour de force in mathematical physics and he has been called a
founder of mathematical astronomy.**

Arlie Petters emigrated to the U.S. in 1979 and he has been a U.S. citizen since 1990. He earned his B.A./M.A. Hunter College - CUNY, 1986 (Mathematics, with additional major in Physics). During the summers, 1986-90 he was a Member of Technical Staff at Bell Laboratories (Lucent Technologies). He earned his Ph.D. in Mathematics from M.I.T (Massachusettes Institute of Technology-1991). From 1991-93, he was an Instructor of Pure Math at M.I.T. Dr. Arlie Petters has been a Visiting Mathematician at Oxford University Mathematical Institute, the Max-Planck-Instute für Astrophsik, and the Geometry Center of The University of Minnesota. From 1993-1998, Dr. Petters was an Assistant Professor in Mathematics at Princeton University and during 1996 to 1998 he served as co-Director of Graduate Studies in Mathematics.

In 1998, Petters was awarded Mathematics most prestigious Sloan
Research Fellowship as well as a 5 year National Science Foundation
Career Grant. In the fall of 1998, Dr. Arlie Petters joined Duke
University, where he holds the William & Sue Gross Chair in
the Mathematics Department where he is **the first African American
tenured** faculty in the sciences/mathematics.

In 2003, he became a Full Professor at Duke University and
is the first black elected

to Duke's prestigious Bass Society of Fellows..

In November 2002, he became the **first recipient of the Blackwell-Tapia Prize**
(**acceptance speech**).

His personal home page: **http://www.math.duke.edu/~petters/**

Email: petters@math.duke.edu

AWARDS

William and Sue Gross Endowed Chair (1998-2003)

CAREER Grant Award - National Science Foundation (1998-2003)

Alfred P. Sloan Research Fellowship (1998-2002)

Belizeans in Solidarity Award for Outstanding Academic Achievement
(1996)

Sigma Xi (Elected 1992, MIT Chapter)

Bell Labs Cooperative Research Fellowship Award (1986-1991)

Hall of Fame of Hunter College (CUNY) for his research work in
mathematical physics

Blackwell-Tapia
Prize (2002)

RESEARCH NOTES

Dr. Petters is chiefly interested in the Mathematical Theory of Gravitational Lensing and related areas (Singularity Theory, General Relativity, Theoretical Astrophysics). He has published 30 papers and one book, chiefly in the area Gravitational Lensing. It has been said that he founded the field of Mathematical Astronomy. DBelow is his research statement.

"Currently, I am working on developing a general mathematical theory of light deflection in weak gravitational fields, and investigating the observational consequences of the theorems in such a theory. This is done by addressing a series of problems touching on several aspects of gravitational lensing: multiple imaging, magnification, critical curves and caustics, and mass reconstruction. These issues are treated not only for the single lens plane case, but for any finite number of lens planes. My goal is to emphasize the stable and generic features of lensing, drawing conclusions essentially independent of the details (especially, the oversimplifying approximations and assumptions) of a chosen lens system model. To obtain such "universal'' results, one must employ tools from singularity theory. At the same time, I also analyze in-depth specific models that are physically realistic. My research involves collorations with mathematicians, astrophysicists, and computer scientists."

A first step towards the aforementioned mathematical
theory appears in the book: **Singularity Theory and Gravitational
Lensing**.

**BOOKS**

**A. O. Petters**, H. I. Levine, and J. Wambsganss __Singularity
Theory and Gravitational Lensing__, BirkhSuser, Boston, **2000.**

**SELECTED PUBLICATIONS**

**In Press:**

1. C. Keeton, S. Gaudi, and A. O. Petters, __Identifying Lensing
by Substructure I. Cusp Lenses__, submitted (2002). See astro-ph/0210318
.

2. A. O. Petters, __On Relativistic Corrections to Microlensing
Effects: Applications to the Galactic Black Hole__, MNRAS (2002).
In press. See astro-ph/0208500 .

**PUBLISHED**

- (with S. Frittelli),
__Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing__,*J. Math. Phys.,*, November (2002).**43** - (with B. S. Gaudi),
__Gravitational Microlensing Near Caustics I: Folds__,*Astrophys. J.,*, 970 (2002).**574** __Stable Lens Systems, Lensed Image Magnification, and Magnification Cross Sections__,*Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity*, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001).- (with S. Frittelli),
__Wavefront Singularities due to an Elliptical Potential__,*Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity*, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001). - (with B. S. Gaudi),
__Center of Light Curves for Whitney Fold and Cusp__*Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity*, eds. V. Gurzadyan, R. T. Jantzen, and R. Ruffini (World Scientific, Singapore, 2001). - (with H. I. Levine and J. Wambsganss),
__Singularity Theory and Gravitational Lensing__, Birkhauser, Boston, 2000. - (with F. J. Wicklin)
__Fixed Points Due to Gravitational Lenses__, J. Math. Phys.,**39**, 1011 (1998). __Some Global Results on Gravitational Lensing__,*Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity*, ed. R. Ruffini (World Scientific, Singapore, 1997).- (with S. Mao, and H. Witt),
__Properties of Point Mass Lenses on a Regular Polygon and the Problem of Maximum Number of Lensed Images__,*Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity*, ed. R. Ruffini (World Scientific, Singapore, 1997). See astro-ph/0708111. - (with F.J. Wicklin),
__Counting Formulas and Bounds on Number of Fixed Points Due to Point-Mass Lenses__, Proceedings of the Eighth Marcel Grossmann Meeting on General Relativity 1997, ed. R. Ruffini (World Scientific, Singapore). __Multiplane gravitational lensing: III. Upper bound on number of images__*,*J. Math. Phys.**38**(1997), 1605--1613.__Curvature of Caustics and Singularities of Gravitational Lenses__, Proceedings of the Second World Congress of Nonlinear Analysts ed. V. Lakshmikantham (Elsevier Science Ltd., Oxford, 1997).- (with F.J. Wicklin),
__New Caustic Phenomena for Caustics in Double-Plane Lensing__,*Astrophysical Applications of Gravitational Lensing*, ed. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996). __Mathematical Aspects of Gravitational Lensing__, in*Proceedings of the Seventh Marcel Grossmann Meeting on General Relativity*, vol. B, eds. R. T. Jantzen and G. M. Keiser (World Scientific, Singapore, 1996).__A Cusp-Counting Formula for Caustics due to Multiplane Gravitational Lensing__, in*Astrophysical Applications of Gravitational Lensing*, ed. C. S. Kochanek and J.N. Hewitt (Klumer Academic, Dordrecht, 1996).- (with H. J. Witt)
__Bounds on number of cusps due to point mass gravitational lenses__*,*J. Math. Phys.**37**(1996), 2920--2933. __Lower Bounds on Image Magnification in Gravitational Lensing__,*Proc. R. Soc. Lond. A,*, 1 (1996).**452**- (with F.J. Wicklin),
__Caustics of the Double-Plane Two Point-Mass Gravitational Lens with Continuous Matter and Shear__,*Mon. Not. R. Astron. Soc.,*, 1399 (1995).**277** __Multiplane gravitational lensing: II. Global geometry of caustics__*,*J. Math. Phys.**36**(1995), 4276--4295.__Multiplane gravitational lensing: I. Morse theory and image counting__*,*J. Math. Phys.**36**(1995), 4263--4275.- (with H. Levine),
__Singularities and Gravitational Lensing__, in*Passion des Formes: Hommage a' Rene' Thom*, vol. 1, ed. M. Porte (E.N.S. Edition, Fontenay-St Cloud, 1994). - (with H. Levine and J. Wambsganss)
__Applications of singularity theory to gravitational lensing: I. Multiple lens planes__*,*J. Math. Phys.**34**(1993), 4781--4808. - (with H. Levine),
__New Caustic Singularities in Multiple Lens Plane Gravitational Lensing__,*Astron. Astrophys.,*, L17 (1993).**272** __Arnold's Singularity Theory and Gravitational Lensing__,*J. Math. Phys.,*, 3555 (1993).**34**- (with Hans J. Witt)
__Singularities of the one- and two-point mass gravitational lens__*,*J. Math. Phys.**34**(1993), 4093--4111. - (with D. Spergel)
*An Analytical Approach to Quasar Variability due to Microlensing in Gravitational Lenses*, , in*Gravitational Lenses*, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics**406**, Springer, Berlin, 1992). __Morse theory and gravitational microlensing__, J. Math. Phys.**33**(1992), 1915--1931.**ALSO**in ,*Gravitational Lenses*, eds. R. Kayser, T. Schramm, and L. Nieser (Lecture Notes in Physics**406**, Springer, Berlin, 1992).

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